Advertisements
Advertisements
Question
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Advertisements
Solution
`int sqrt(x^2 + 2x + 10) "d"x = int sqrt((x + 1)^2 + 1^2 + 10) "d"x`
= `int sqrt((x + 1)^2 + 9) "d"x`
= `int sqrt((x + 1)^2 + 3^2) "d"x`
Put x + 1 = t
dx = dt
= `int sqrt("t"^2 + 3^2) "dt"`
= `"t"/2 sqrt("t" + 3^2) + 3^2/2 log |"t" + sqrt("t"^2 + 3^2)| + "c"`
= `"t"/2 sqrt("t"^2 + 3^2) + 3^2/2 log |"t" + sqrt("t"^2 + 3^2)| + "c"`
= `((x + 1))/2 sqrt((x + 1)^2 + 3^2) + 3^2/2 log |x + 1 sqrt((x + 1)^2 + 9)| + "c"`
= `((x + 1))/2 sqrt(x^2 + 2x 1 + 9) + 9/2 log |x + 1 + sqrt(x^2 + 2x + 1 + 9)| + "c"`
= `((x + 1))/2 sqrt(x^2 + 2x + 10) + 9/2 log |x + 1 + sqrt(x^2 + 2x + 10)| + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the following functions with respect to x :
sin2 5x
Integrate the following functions with respect to x :
`"e"^(x log "a") "e"^x`
Integrate the following with respect to x :
`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`
Integrate the following with respect to x:
x log x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^x ((2 + sin 2x)/(1 + cos 2x))`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Find the integrals of the following:
`1/sqrt((2 + x)^2 - 1)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Choose the correct alternative:
The gradient (slope) of a curve at any point (x, y) is `(x^2 - 4)/x^2`. If the curve passes through the point (2, 7), then the equation of the curve is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int "e"^(- 7x) sin 5x "d"x` is
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
